The issue with this example (and many similar ones) is that to decide between interventions on a variable X from the outside, EDT needs an additional node representing that outside intervention, whereas Pearl-CDT can simply do(X) without the need for an additional variable. If you do add these variables, then conditioning on that variable is the same as intervening on the thing that the variable intervenes on. (Cf. section 3.2.2 "Interventions as variables" in Pearl's Causality.)